Abstract
One obtains generalizations and refinements of ergodic and mixing theorems [Yu. V. Linnik, Ergodic Properties of Algebraic Fields, Springer-Verlag, New York (1968)] for the distribution of integral points on a two-sheeted hyperboloid. One gives a survey of the applications of the discrete ergodic method to indefinite ternary quadratic forms; in particular, one describes the results of the papers of A. M. Istamov, E. V. Podsypanin, A. V. Malyshev, and U. M. Pachev, published in this issue.
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